Question

The lengths of the sides of a triangle are in the ratio 5 : 6 : 7. Describe the length of the longest side if the perimeter is less than 54 cm.

Answer 1

5n+6n+7n=18n

18n<54

n<54/18

n<3

7*3=21 for the longest side.

Thus the longest side is less than 21.

Hope this helps

Answer 2

The perimeter of a shape is the summation of the visible lengths of the shape. The length of the longest side of the triangle is less than 21 cm

Let the three sides of the triangle be a, b and c.

So;

$a : b : c = 5 : 6 : 7$

The longest ratio is 7. So, the longest side is c.

Calculate the total ratio

$Total = a + b + c$

$Total= 5 + 6 + 7$

$Total= 18$

Given that the perimeter is less than 54cm.

This means that the longest side (c) is calculated as follows:

$c < \frac{c\ ratio}{Total} \times Perimeter$

So, we have:

$c < \frac{7}{18} \times 54cm$

$c < 7 \times 3cm$

$c < 21cm$

Hence, the longest side is less than 21 cm

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